What metaphysics can plausibly back up the claim that God became incarnate? In this essay we investigate the main kinds of models of incarnation that have been historically proposed. We highlight the philosophical assumptions in each model, and on this basis offer novel ways of grouping them as metaphysical rather than doctrinal positions. We examine strengths and weaknesses of the models, and argue that ’composition models’ offer the most promising way forward to account for the pivotal Christian belief that, in Christ, true divinity and true humanity meet in a genuine union